After premiering three new tracks at their tour-opening show in Milan, U2 introduced fans to another song, titled “Every Breaking Wave,” in Helsinki on Saturday. “Like every breaking wave on the shore, this is as far as I can reach,” Bono sang during the soaring acoustic number. “No one has heard that before — not even us,” he later told the crowd. Watch video of “Every Breaking Wave” above.

“Every Breaking Wave” was originally intended for No Line on the Horizon, U2 told Rolling Stone in March of last year, but was later decided as the first single for U2’s follow-up Songs of Ascent. The band has also debuted “Return of the Sting Ray Guitar,” “North Star” and “Glastonbury” on the European leg of their 360 Tour. The band will be performing through October 8th, giving them plenty of opportunities to debut some of the “four new albums’ worth” of material they have has stored up in recent years, as the band told RS David Fricke backstage at their Milan show. In addition to Songs of Ascent and the Spider-man: Turn Off the Dark Broadway musical, U2 are also working on a “rock album” and a “club-sounding album.” Bono predicts that by the time their tour reaches the U.S. in 2011, “Those people are going to have tickets to a whole new show with new songs.”

In other U2 news, the band announced today that Jay-Z will open for them on the Australian and New Zealand legs of their 360 Tour, which begins November 25th. U2 and Jay-Z have previously paired up for a performance of “Sunday Bloody Sunday” at the 2009 MTV European Music Awards, and recorded the Haiti earthquake benefit single “Stranded (Haiti Mon Amour).”

For more on U2, be sure to check out David Fricke’s backstage report from U2’s Milan concert in the new issue of Rolling Stone, on stands now.